Where are the international financial institutions when you need them? That's one question that G20 leaders will surely ask when they meet in Washington this weekend for talks on the global financial crisis. Alarmingly, the World Bank and the International Monetary Fund, created at the end of the second world war to prevent a repeat of the Great Depression, lack the resources and legitimacy to make a difference in the 21st century. Fortunately, there is a straightforward solution: a Grand Bargain whereby the emerging market economies with substantial reserves infuse the so-called Bretton Woods institutions with cash in exchange for a much greater say in what these institutions do and how they do it.

During the boom, there seemed little need to increase the financial clout of the IMF, despite the risk associated with surging cross-border capital flows. The World Bank, meanwhile, saw demand for its loans decline, as Brazil and other formerly big borrowers enjoyed high private capital inflows and accumulated reserves.

As a result, the international financial institutions became bit-players in global finance. The World Bank, once among the planet's top 10 financial institutions in terms of capitalisation, fell to a spot just barely in the top 100. The bank's last approved capital increase in 1988 brought its capital base to $171bn, an amount dwarfed by the rapid growth of the global economy but still more than enough to handle demand for its traditional loan product. The IMF, meanwhile, has just $250bn to lend globally in response to the current crisis – barely one-third of what the United States has set aside for its own bail-out, not counting outlays to rescue AIG and Fannie Mae and Freddie Mac.

Compounding these institutions' financial decline was a loss of legitimacy, as the United States and Europe continued to call the shots, even as their relative importance in the global economy declined. The effect on the IMF has been striking – with the US Federal Reserve arranging for central bank swaps for Brazil, Mexico, and Korea in a move uncoordinated with the IMF, and with Iceland, Pakistan and Turkey reluctant to ask the IMF for help.

When your house is on fire, it's a hell of a time to discover that the fire department isn't up to snuff. But it's not a bad time at all to start thinking of the benefits to the neighborhood of preventing future conflagrations. Though IMF conditionality in the 1990s was viewed as intrusive and often misguided, multilateral economic conditionality is still preferable to the political conditionality that would arise with bilateral bail-outs.

Two things are needed to make the international financial institutions once again relevant and effective: more money and an improved governance structure that gives the developing world – and especially the huge emerging market countries – much greater say in the key decisions.

The IMF needs higher financial commitments from reserve-rich countries, including China, both to help countries cope with the greater volatility that global capital markets imply, and as a stabilising force for the global financial system. The World Bank has plentiful resources for the traditional loans but little flexibility to use its resources countercyclically, and no call at all on the grant financing it needs to jumpstart regional and global programmes.

These complementary needs – money and governance – can form the basis of a Grand Bargain: the United States and Europe should offer developing countries much greater voice in how the World Bank and IMF are run in exchange for urgently needed capital infusions from countries with large capital reserves.

China has the biggest reserves – some $2tn – but Brazil, Russia, India, the Gulf oil states and some others also have the resources that would allow them to be substantial contributors to the IMFs and World Bank's capital base.

Why should these countries invest in stronger multilateral financial institutions? Not only for the enhanced national prestige of helping to call the shots (although this can't be entirely discounted, either). More importantly, they are struggling with very big and complex problems that no country can solve alone. The international financial institutions, for all their shortcomings, are the best mechanism yet devised for organising collective action to solve these problems, that is, to provide what we economists like to call global public goods.

The current financial crisis has vividly shown us that in a highly interconnected global economy financial sector stability and access to credit are crucial global public goods. Because one major economy can quickly destabilise the entire system, it's in everybody's interest to have effective tools for spotting problems before they get out of hand, and for responding to crises when they do occur.

Moreover, financial sector instability isn't the only global crisis requiring collective action where economics, finance and technical knowledge are critical to an effective international response. Two closely related challenges of urgent concern to the developing world – climate change and the global food crisis – can only be addressed with shared investments.

The financial crisis has levelled the international playing field in unexpected ways. Interdependence and the need for collective action to solve common problems are more clearly evident now than ever before.

The large emerging market countries that will be represented at the G20 have an opportunity to press for changes in the governance of the global financial institutions to make them more responsive to developing country needs, in exchange for urgently needed financial infusions. The US and Europe have an opportunity to lock in a rules-based approach to international finance in exchange for votes and power in institutions otherwise at risk of permanent atrophy. Let the conversation about a 21st century Grand Bargain begin.